Since 2000, aid dependency has fallen in Ghana from 46% to 27%. Photograph: Delphine Ramond/AFP

Prime ministers and presidents generally don't like global summits. They are a necessary part of the ebb and flow of international diplomacy. But frankly, the majority of summits don't achieve that much – they usually end in a bland bureaucratic statement which nudges things forward to the next summit. Summits with genuine, long-lasting outcomes are rare. But as we started planning for the Gleneagles G8 meeting in 2005, I saw that it could be one of these rare ones – a summit about changing the world, not changing the wording on a communique.

I decided to put Africa at the top of the agenda for Gleneagles, helped immeasurably by the incredible Make Poverty History campaign and particularly Bono and Bob Geldof, who assisted and prodded and kept everyone on their toes. And it worked. Today, the positive legacy of that summit is still being felt across Africa: aid was doubled and developing world debt dropped.

Yet for me, half of the Gleneagles story remains untold. The Commission for Africa, and its championing of good governance and growth, was overshadowed by the immense achievements on aid and debt. After leaving office, I set up the Africa Governance Initiative to continue my work on that forgotten half. Here, I would like to explain why. But first, I want to answer the aid sceptics – those who think aid doesn't work or is all swallowed up in corruption. Look at the facts. In Africa since 2005, the rate of children dying before their fifth birthday has fallen by 18%. The proportion of people in Africa living in extreme poverty is down by nearly 10%. Aid from the UK alone has in the last two years helped more than 5 million more children go to primary school and 6 million people to access emergency food supplies.

If the statistics don't convince you, visit Africa and see the change for yourself. Take Liberia. In the same year as we hosted the G8 at Gleneagles, this once war-torn country was holding its first presidential election in a generation. Today, when I visit the capital, Monrovia, I can see tangible examples of the impact of well-used aid money, from an airport which now handles flights from commercial capitals such as London and New York to new roads and street lights.

And dropping the debt worked too. In its report to be launched this week, Bono's ONE Foundation sets out the difference the debt relief has made. So far, 35 countries, mostly in Africa, have had their debts completely cleared – adding up to over $35bn. And the money that would once have gone on interest payments has been well used in most cases – increasing the amount spent on reducing poverty in these previously indebted countries by an average of 3% of GDP.

But when I look back at what we achieved in 2005, I believe the most important story is yet to be told. The financial commitments made by the rich countries in 2005 were historic and, while they haven't always been fully met, the money which has arrived has improved hundreds of thousands of lives. Yet when my government looked at what would deliver real and sustainable change, and when I spoke to African leaders before Gleneagles, it was clear that aid alone wasn't the answer. It couldn't simply be about the money. That is why a year before the summit I set up the Commission for Africa to look at this bigger picture, including – most crucially for me – effective governance and economic growth.

If the last decade of development progress was defined by aid, the next will be defined by governance and growth. By governance, I don't just mean transparency, as important as that is, but also the ability of governments in developing countries to get things done. To deliver the life-changing improvements their citizens expect. Since leaving office, I have focused on this issue through the Africa Governance Initiative, which works alongside political leaders to help them reform their systems to implement development plans and tackle poverty.

Take the plan to deliver free health care for pregnant mothers and young children in Sierra Leone. Previously, the money and the vision were in place, but the institutional capacity to implement reform was lacking. But with the support of donors, not least the Department for International Development, President Ernest Bai Karoma was able to put strong monitoring processes in place and ensure that the policy was driven from the centre of government until delivery was achieved. The result was more efficient and cost-effective drug procurement and dissemination, more health centres equipped and staffed and, ultimately, more lives saved. For example, there has been a 60% reduction in maternal mortality in government health centres since the reforms.

Alongside governments that work, Africa needs markets that deliver – creating jobs and improving living standards. Every country that has achieved rapid reductions in poverty has done so with a growing economy and high levels of private sector investment. Africa is now at this stage – the development tipping point. As the west struggles to get single digit growth, African countries are nearing double digits. Africa is among the fastest-growing regions in the world. The Gleneagles agreement can claim some credit for this; bilateral aid for trade to sub-Saharan Africa has almost doubled between 2005 and 2011. Foreign direct investment in the continent has increased by 87% in the past 10 years; in East Africa alone FDI was $1.7bn in 2010. African countries no longer depend on foreign aid to keep their heads above water; now they are investing to grow – particularly in areas such as roads and energy. If Africa continues to grow and continues to improve its governance, we have the chance to fundamentally change the nature of the relationship between Africa and the rest of the world. We can end the old donor-recipient relationship and replace it with a genuine partnership.

This is what African leaders want. The presidents of Sierra Leone, Liberia and Rwanda, for example, have all set out plans to move beyond aid dependence. And it is achievable. Since 2000, aid dependency has fallen in Ghana from 46% to 27%, in Rwanda from 86% to 65%. Looking at low-income countries specifically, on average their aid dependency has fallen by a third in this period. Ghana, for example, is on track to be totally free of aid in the next decade. I have said I believe Africa can be free of dependence on aid within a generation. I stand by that. It's ambitious but achievable.

The very fact that people are still talking about Gleneagles eight years on shows that we were right to be ambitious, to change the debate. Of course, the arguments on development have got even tougher since, as budgets are squeezed across Europe as a result of the financial crisis. But it is to the great credit of the British people and David Cameron's government that even in these circumstances they have kept up their support for Africa and development.

The communique after Gleneagles said: "This is a moment of opportunity for Africa. Its leaders have embraced a new vision for the continent's future which recognises their leading role in addressing the continent's challenges and realising its opportunities." The journey from Gleneagles to long-lasting development in Africa is not over. But Africa is on the move and if we keep going on the whole Gleneagles agenda – maintain aid but remembering governance and economic growth – the continent will be transformed. So I'm proud to say that Gleneagles has turned out to be that rare thing – a summit that matters.